Parades seem best enjoyed while watching rather than participating. However, I think everyone should participate at least once for the experience.
Kurt's post about using the spark advance for speed control is excellent. Assuming your car is not one prone to overheating, this works excellent.
Also, agree with everyone's info about servicing the horn prior to the parade. However, be courteous with it. The people in the parade in front of you might not enjoy it as much as the crowd. In my experience, the crowd will prompt you when an 'ahooga' is needed. Keep em short, the marching girl scouts in front of you will appreciate it.
Since we're talking about servicing... Make sure your car idles reliably! If your car won't idle reliably and slowly, then do yourself and your car a favor and sit this one out. Make sure you don't have any vacuum leaks and that your carb is adjusted well. A rough idle or having to fight the motor to keep it running will greatly detract from the fun.
I know you have a Tudor, but this is for those that have a coupe with a rumble seat- put something or someone in it. If you don't have some kids that like to wave for an hour straight to put in it, find some. The scouts or FFA or 4-H will usually be a good place to recruit some wavers. If you can't find kids, get a large stuffed animal.